Chaos Theory and ComputersDate: 2/4/96 at 17:35:0 From: Anonymous Subject: Chaos Theory I am not really trying to get the answer to a question, I am merely trying to make sense of a formula. I go to Cunningham Middle School in Presque Isle, Maine, and have recently been studying chaos theory. I have happened upon an equation that can create a fractal that demonstrates the theory graphically. Now, since the computer cannot learn, and chaos theory is based on a lack of pattern, how is the computer able to compute this? The equation contains the x and y coordinates (making it 2D), but this is something I am unable to comprehend - i. Isn't the variable i an imaginary number? How is the computer able to use its pattern-based Operating System and FPUs to generate the algorithms associated with the variable i? It seems as if either the fractal (or graph, really) is off base, or the entire OS is off base. Any ideas? Date: 2/5/96 at 9:53:22 From: Doctor Ethan Subject: Re: Chaos Theory Hello, Well, I can try to help you out. First, let's deal with the imaginary number issue. In this case i is not a variable. i is the notation for the Square root of -1 so i is defined by i * i = -1. So, although the computer probably cannot inherently do complex arithmetic, it would be easy to design a program that could. Now on to your other questions. You are right, the computer doesn't learn anything, and to a degree you are right that Chaos lacks pattern. However, if you have a formula that is chaotic (and some pretty simple ones are) then the computer doesn't need to do anything but follow the formula. It is the formula rather than the computer that is chaotic. I can't say much about the actual formula since I don't know what it is; however, many chaos patterns are generated by recursion, which means doing the same process over and over. Computers are very good at this, and they allow us to do the same things over and over thousands of times. This means that we can follow these patterns to see if they become chaotic. I hope this has helped a little. If you want more help, write back and maybe send us the formula that you have been using. -Doctor Ethan, The Math Forum |
Search the Dr. Math Library: |
[Privacy Policy] [Terms of Use]
Ask Dr. Math^{TM}
© 1994- The Math Forum at NCTM. All rights reserved.
http://mathforum.org/dr.math/